Question

Write the following sum using summation notation -2/5+3/6-4/7........11/14

Answer 1

`\sum_(n=1)^(10)(-1)^n\left ( (n+1)/(n+4) \right )`

Explanation:

Given:
`(-2)/(5)+(3)/(6)-(4)/(7)+...+(11)/(14)`

To write: the given expression using summation notation

Solution:

Summation notation helps to write a long sum as a single expression.

In the summation notation, the variable
`\sum` is called the index of summation.

Let
`x_1,x_2,x_3,...,x_n` denote a set of n numbers.

Then in summation notation,

`x_1+x_2+x_3+...+x_n=\sum_(i=1)^(n)x_i`

`(-2)/(5)=(-1)^1\left ( (1+1)/(1+4) \right )\\(3)/(6)=(-1)^2\left ( (2+1)/(2+4) \right )\\(-4)/(7)=(-1)^3\left ( (3+1)/(3+4) \right )\\.\\.\\.\\(11)/(14)=(-1)^10\left ( (10+1)/(10+4) \right )\\\therefore (-2)/(5)+(3)/(6)-(4)/(7)+...+(11)/(14)=\sum_(n=1)^(10)(-1)^n\left ( (n+1)/(n+4) \right )`